Private Language and Logicism

Starting at #243 in the Investigations, Wittgenstein presents a sequence often characterized as his 'private language argument', a potentially misleading formulation, since he opposes, not defends that possibility.  His analyses in those passages show that while experiences, such as pains, may be private, the language associated with them is not.  such demystification seems to exemplify what he calls 'showing the fly the way out of the fly-bottle', i. e. it functions as a corrective to an extant problem.  In contrast, a preemptive approach, i. e. what might be characterized as 'preventing the fly from entering the bottle to begin with', argues, as has been proposed here, that all Language is essentially a medium of Communication, which entails that essentially no Language is private.  Now, it seems difficult to deny that the language of a Solipsist is private, and, furthermore, it seems to follow from the sequence of #5.62 to #5.6331 of the Tractatus that the Language examined in that work is that of a Solipsist, i. e. a language of one for whom "the world is my world".  Thus, even if the Private Language Argument presented in the Investigations does not explicitly cite Logicism, it seems, at minimum, applicable to it.  In contrast, the preventative alternative proposed here leaves no doubt in that regard.